Sarl Rae Manual

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South African Radio League

Radio Amateur Examination Study Guide

REVISED NOVEMBER 2007

Copyright South African Radio League 2007

This study guide may be copied for individual use by students studying for the

Amateur Radio License. Permission from the South African Radio League isrequired for all other use of the material.

WE ACKNOWLEDGE WITH THANKS THE ORIGINALCOMPILATION OF THIS STUDY GUIDE BY ANDREW ROOS IN

2005


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Table of Contents

Chapter 1 - Introduction to Amateur Radio............................................................................... 1 Chapter 2 - Basic Electrical Concepts....................................................................................... 5

Chapter 3 - Resistance and Ohm’s Law .................................................................................... 9 Chapter 4 - The Resistor and Potentiometer............................................................................ 13 Chapter 5 - Direct Current Circuits ......................................................................................... 18 Chapter 6 - Power in D.C. Circuits.......................................................................................... 27 Chapter 7 - Alternating Current............................................................................................... 31 Chapter 8 - Capacitance and the Capacitor ............................................................................. 39 Chapter 9 - Inductance and the Inductor ................................................................................. 47 Chapter 10 - Tuned Circuits .................................................................................................... 52 Chapter 11 - Decibel Notation................................................................................................. 60 Chapter 12 - Filters.................................................................................................................. 65 Chapter 13 - The Transformer................................................................................................. 72 Chapter 14 - Semiconductors and the Diode........................................................................... 78 Chapter 15 - The Power Supply .............................................................................................. 89 Chapter 16 - The Bipolar Junction Transistor ......................................................................... 94 Chapter 17 - The Transistor Amplifier.................................................................................... 99 Chapter 18 - The Oscillator ................................................................................................... 107 Chapter 19 - Frequency Translation...................................................................................... 116 Chapter 20 - Modulation Methods ........................................................................................ 124 Chapter 21 - The Transmitter ................................................................................................ 137 Chapter 22 - Receiver Fundamentals .................................................................................... 142 Chapter 23 - The Superheterodyne Receiver......................................................................... 149 Chapter 24 - Transceivers and Transverters.......................................................................... 158 Chapter 25 - Antennas ........................................................................................................... 161

Chapter 26 - Propagation....................................................................................................... 182 Chapter 27 - Electromagnetic Compatibility......................................................................... 189 Chapter 28 - Measurements................................................................................................... 200 Chapter 29 - Digital Systems................................................................................................. 207 Chapter 30 - Operating Procedures ....................................................................................... 234 FORMULA SHEET .............................................................................................................. 253


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Radio Amateur Examination Study Guide Chapter 1 - Introduction to Amateur Radio

Copyright © South African Radio League 2007 - Revised November 2007 1

Chapter 1 - Introduction to Amateur Radio

Amateur radio is a hobby that involves experimenting with radio (and related technologies

like television or radar) for fun and education. It is also known as “Ham Radio” and radio

amateurs are sometimes referred to as “hams”. Like most hobbies, there are many different

activities that fall under its umbrella.

Communicating with other Radio Amateurs

Using radio to communicate with other amateurs is one of the foundations of the hobby. Most

amateurs have a radio station of their own, which can range from a simple single-band

handheld transceiver (a combination of a transmitter and a receiver is known as a transceiver )

for talking to others in the same town, to a sophisticated station that is capable of worldwide

communication. Many clubs also have club stations that are available for use by club

members.

Radio amateurs communicate in many different modes. The most common are by voice

(known as phone although it does not use the telephone system), Morse code (also referred to

a CW ) and various digital modes including slow-scan television. The contents of an amateurcommunication (known as a QSO) range from the briefest exchange of name and location, up

to long conversations (known as rag-chews) that may last an hour or more.

Amateur radio is not like the phone system since you generally can’t dial a particular station.

If you want to speak to a particular person, then you must agree a time and a frequency where

you will meet – this is known as a schedule, or “sked” for short. Otherwise you can just speak

to whoever happens to be listening and is interested in a chat, which is a great way to make

new friends. There are also some regularly scheduled networks (or “nets”) where operators

who share a common interest get together at a particular time and frequency to exchange

ideas.

Collecting QSL CardsAfter communicating with another amateur (especially one in a foreign country) it is

customary to send a QSL card, which is a postcard-sized card with information about yourself

and your station, and details of the QSO such as the date, time, frequency, mode and the

callsign of the station worked. Many amateurs take a great deal of pride in their QSL cards,

which are works of art. As well as being something to display and a nice reminder of the

contact, QSL cards are often required if you wish to claim a contact for an award (see below).

Building Radio and Electronics Equipment

Many amateurs build at least some of their equipment. Some build equipment from purchased

kits or from plans found in amateur radio magazines. Others build their equipment from

scratch, doing all the necessary design and sourcing the components themselves. The

complexity ranges from simple projects, such as a computer soundcard interface that can be built in an evening to complete radio transmitters and receivers that may take months or years

of work. Today microprocessors and digital signal processing (DSP) is an increasingly

important part of the hobby, so building equipment may also involve writing the necessary

micro-controller or DSP programs. Of course if you do not enjoy electronics, then everything

you need to participate in the hobby can be purchased off the shelf.

Building Antennas

Most amateurs build at least some of their own antennas. Antennas may range from a simple

wire antenna suspended from a tree, to a complex multi-element beam sitting on top of a large

tower. Antenna projects can be very rewarding as good results may be obtained from fairly

simple designs. There are a number of software packages available that allow you to design

an antenna and model its performance before you invest in the construction of the antenna.


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Public Service and Emergency Communications

Radio amateurs have a proud history of making their skills and equipment available for public

service and emergency communications. On the public service side, amateurs provide

communications for many sporting events such as rallies, marathons and cycle tours where

their ability to communicate effectively from remote places is of great assistance to the

organizers.

Many amateurs also ensure that their radio stations have some alternative power source

(which could be batteries, a generator, or solar power) so that they can continue to provide

communications in the event that a natural disaster disrupts the telephone and power

distribution systems. In South Africa, Hamnet, a special interest group of the South African

Radio League, coordinates amateur emergency communications.

DX'ing

“DX'ing” means communicating with as many different places as possible, often in order to

qualify for certificates and awards. (The term comes from the use of “DX” as an abbreviation

for “long distance”.) There are many different awards, including:

The DXCC (DX Century Club) certificate, which you qualify for by communicating

with 100 or more different countries.

The Worked All ZS award, for contacting 100 stations in the various regions of South

Africa (the award’s name comes from the fact that “ZS” is one of the callsign prefixes

assigned to South African radio stations).

The Islands on the Air (IOTA) awards, which are given for communicating with

stations located on islands.

The Summits on the Air (SOTA) awards for communicating with mountaintop

stations.

DXpeditions

Because DXers are always on the lookout for countries, islands, mountains or provinces that

they have not worked before, there is often a flurry of interest and activity when a rare

country or island is “activated” by some intrepid radio amateur setting up a station.

Expeditions to unusual places for the purpose of setting up and operating a radio station there

are called “DXpeditions”, and participating in DXpeditions is itself a very rewarding and

challenging activity.

Contests

Contests bring out the competitive nature of some radio amateurs, who enjoy the challenge to

contact as many different stations as possible over a predetermined period of anything froman hour or two up to 48 hours. Contests may be run on a local, national, regional or

international basis and may attract anything from 10 to 5 000 contestants. Many contests have

several entry categories to allow similarly equipped stations to compete amongst each other.

Satellite Communications

The amateur community has successfully launched a number of small communications

satellites for the use of radio amateurs around the world. Communicating with other amateurs

via satellite (or via the earth’s natural satellite, the moon) gives radio amateurs an

unparalleled opportunity to learn about the technology that underlies much of the modern era

of communications. Because amateurs themselves develop these satellites as a cooperative,

non-profit venture, those who are interested in the design and construction of satellites also

have the opportunity to study the designs and may eventually be able to contribute to new

amateur satellite projects.


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Maritime and Off-Road Communications

The maritime and off-road communities are increasingly turning to amateur radio for their

communication needs. Thousands of small craft such as yachts make use of the services

provided by maritime nets which pass on weather reports and crucial safety information,

allow mariners to access email and assist in the search for missing boats. Off-roaders who

venture into uninhabited areas can also benefit from amateur communications, both betweenvehicles within a party and also back to a “home base” or to summon assistance in an

emergency.

License Requirements in South AfricaIn order to operate an amateur radio station you must have a license issued by the

Independent Communications Authority of South Africa, ICASA. When you are issued with a

license you will also be given a unique callsign. Every amateur has a callsign, which is used

to identify him or her on the air. South African amateur callsigns consist of the letters “ZU”,

“ZR” or “ZS” followed by a single digit indicating the region of the country in which you are

located, followed by one to three letters. Using the callsign “ZS1AN” as an example, the

“ZS” indicates that it is an Unrestricted license, the “1” shows that the holder resides in the

Western Cape, and the letters “AN” distinguishes the holder from all the other holders of an

unrestricted license in the Western Cape. Every time you make a transmission from an

amateur radio station you are required to identify yourself using your callsign. There are three

different classes of license:

The Entry Level (ZU) License

The Entry level license is a simple entry point into the hobby. It has restricted privileges in

the High Frequency (HF) and Very High Frequency (VHF) bands, with a maximum power

output of 20 W for single sideband (voice) transmissions. In order to obtain a Novice license

you must pass a (Class B) Radio Amateurs’ Examination

The Restricted (ZR) License

The Restricted license has full privileges on the Very High Frequency (VHF) and Ultra High

Frequency (UHF) bands, which are typically used for short-range communication and for

communication via satellite. ZR licence holders have restricted access to HF frequencies

with a power limit of 20 dBW

To obtain a Restricted (ZR) license you must pass the full (Class A) Radio Amateur’s

Examination. This is the study material for the Class A examination, so if you pass the

examination at the end of the course you will be entitled to a Restricted license. Restricted

licenses have callsigns beginning with “ZR”.

The Unrestricted (ZS) License

The Unrestricted license has full privileges on all the bands allocated for use by radio

amateurs. In most cases the maximum power output is 400W for single sideband (voice)transmissions. To obtain an Unrestricted license you must pass the full (Class A) Radio

Amateurs’ Examination, as well as furnish proof of your ability to correctly set up, adjust and

operate an amateur HF transceiver. In addition you have to complete an assessment

prescribed by the SARL, the National Body for Amateur Radio, demonstrating advanced

knowledge of theoretical or practical aspects of amateur radio. (Visit www.sarl.org.za for the

details)

The Radio Amateurs’ Examination

The Radio Amateur’s Examination is held twice each year, in May and October. It consists of

two papers: Regulations and Operating Procedures and Technical . The Regulations and

Operating Procedures paper has 30 multiple-choice questions and the Technical paperconsists of 60 multiple-choice questions.


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The examination is set and administered by the South African Radio League, the National

Body for Amateur Radio in South Africa. ICASA is the Independent Communications

Authority of South Africa, a statutory body that regulates the communications industry. The

examination fee changes from time to time, so ask your course instructor what the current fee

is, or consult the website of the South African Radio League, www.sarl.org.za

Restrictions on the Use of an Amateur Radio Station

The Radio Regulations include some restrictions on the use of an amateur radio station. It is

important that you understand these in case you find that what you had planned to do with

your amateur radio license is not permitted!

1. Amateur radio stations may not be used for broadcasting. Amateur radio is intendedfor direct “one-on-one” communications with other amateurs, and not as a

community broadcasting service.

2. Amateur radio stations may only transmit music under very specific conditions,which are intended to ensure that they do not become pirate broadcast stations.

3. No products or services may be advertised on amateur radio.

4. Amateur radio stations may not transmit messages for reward.

5. Amateur radio stations may not be used to transmit business messages that could besent using the public telecommunications service.

6. Amateur radio stations may not be used to transmit indecent, offensive, obscene,threatening or racist comments.

7. Amateur radio stations may not be used to pass third-party traffic (in other words,

messages that originate from anyone other than the amateur who is operating thestation) except during an emergency.

This chapter was intended to give you an idea of what amateur radio is all about, what the

license requirements are, and what legal restrictions there are on what can be transmitted by

amateur radio stations. We hope this will have helped you to decide that amateur radio is a

hobby that you wish to participate in. We would like to take this opportunity to welcome you

to the amateur community and hope that you will find this course interesting and worthwhile.


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Radio Amateur Examination Manual Chapter 2 - Basic Electrical Concepts


Chapter 2 - Basic Electrical Concepts

Atoms and ElectronsThe matter that we interact with every day – solid objects like desks and computers, liquids

like water and gasses like the air we breathe – consists of atoms. Atoms are tiny and invisible

to the naked eye and were once thought to be the ultimate indivisible constituents of matter, but we now know that they are themselves made up of various sub-atomic particles. For the

purposes of this discussion, atoms can be thought of as a very small central nucleus that is

surrounded by a cloud of electrons. Electrons are not simple particles like miniature planets

surrounding the nucleus, but are “smeared out” in space so that even a single electron can

form a cloud around a nucleus.

The nucleus consists of one or more protons, which are positively charged particles, usually

accompanied by some neutrons, which are uncharged (electrically neutral) particles. So the

overall charge of a nucleus is always positive, from the positively charged protons. Electrons

are negatively charged, and since opposite charges attract, the negatively charged electrons

are attracted to the positively charged nucleus, which is what makes the electrons stay close to

the nucleus.

Point to remember: Unlike charges attract, like charges repel.

Of course, since like charges repel, you might ask what stops the positively charged protons

in the nucleus from bursting apart and destroying the atom. The answer is that another force

called the “strong nuclear force” holds the nucleus together. The strong nuclear force is

stronger at the very short distances characteristic of an atomic nucleus than the repulsive

electromagnetic force between the positively charged protons.

Visible amounts of matter contain huge numbers of atoms. For example, a copper cube 1mm

on each side would weigh less than one hundredth of a gram, but would contain about 85 000000 000 000 000 000 atoms!

Conductors and InsulatorsIn some materials, such as copper, some of the electrons are not very strongly bound to their

nuclei. These electrons are free to move around in the material, as long as other electrons

replace them when they move. If they were not replaced then the area they left would have

more protons than electrons, giving it an overall positive charge. This would attract electrons

back there and make it harder for other electrons to leave, since the negatively charged

electrons would be attracted by the positive overall charge.

Materials in which some of the electrons can move around relatively freely conduct electricity

and are known as “conductors”. Materials in which all the electrons are tightly bound to their

nuclei and cannot move around do not conduct electricity and are known as “insulators”.

Most metals are conductors. These include silver (which is the best conductor of all, but too

expensive for most uses), copper (a very good conductor at a more reasonable price),

aluminium (which is ideal for weight-sensitive applications like overhead cables), mercury

(for when you need a good conductor that is a liquid at room temperature) and solder (an

alloy, often of tin and lead, with a low melting point that is used to connect electrical

components together).

Good insulators include most plastics, glass, plexiglass, mica, rubber and dry wood. (Note

that water is not an insulator, so anything wet is likely to conduct electricity, especially if youdid not intend it to.)


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Electric CurrentWhen we speak of a material conducting electricity, we mean that electric currents can flow

through that material. But what is an electric current?

Definition: An electric current is a flow of charge.

Any time that charge is flowing – that is, moving in a relatively consistent direction – there is

an electric current. Since charge is normally associated with particles of one sort or another, a

flow of charge usually entails a flow of charged particles, such as electrons. The particles that

carry the charge are known as “charge carriers”.

The size of an electric current is expressed in amperes, named after the French physicist

André-Marie Ampère (1775-1836) who was one of the pioneers in studying electricity. The

official abbreviation is “A”, but unofficially amperes are often referred to as “amps”.

When an electric current flows through ordinary conductors like copper, the charge carriers

are electrons, so the flow of electric current corresponds to a flow of electrons. However

because electrons are negatively charged, electrons flowing from left to right through a wirewould constitute a negative current flowing from left to right in the wire. This is usually

expressed as a positive current flowing in the opposite direction, from right to left in this case.

So the electric current is generally considered to flow in the opposite direction from the

electrons that carry it!

In order to emphasise this distinction, one may talk about the conventional current that flows

in the opposite direction from the flow of electrons. However whenever someone refers to just

an “electric current” you should assume that they are talking about a conventional current, so

if the charge carriers are negatively charged particles like electrons then the direction in

which the current flows will be the opposite direction to the flow of charge carriers.

You can imagine a (conventional) electric current flowing in a wire to be similar to water

flowing though a pipe. Here the magnitude (size) of the current would correspond to the

volume of water flowing through the pipe each second.

Electric PotentialHaving established that an electric current is a flow of charge, the next question is: what

makes the charge flow? The answer is electric potential. Since unlike charges attract, if you

apply a positive potential to one side of a copper wire and a negative potential to the other

side, loosely bound electrons in the rod will be attracted towards the positive potential and

repelled by the negative potential, causing electrons to move from the negative side to the

positive side. In other words, a conventional current will flow from the positive side of the

wire to the negative side. Electric potential is always measured between two points.

Definition: The electric potential between two points is the amount of energy that it would

take to move one unit of charge from the point of lower potential to the point of higher

potential.

Since energy is measured in Joules and charge in Coulombs, the unit of electric potential is

Joules per Coulomb. This unit is named the “volt” with the abbreviation “V”, named after the

Italian scientist Count Alessandro Volta (1745-1827) who invented the battery. Electric

potential is commonly referred to simply as “voltage”.

Electric potential can be thought of as the pressure that a power source like a pump creates in

the water it pumps through a pipe. The higher the pressure (voltage), the greater the quantity

of water flowing through the pipe per second (current).


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Units and AbbreviationsIf you measure or calculate the amount of something, you usually need to specify the unit of

measurement. For example, if you weigh something and then say that it weighs “10”, this

does not mean very much unless you specify the unit of measurement – 10 grams, or 10

kilograms, or 10 milligrams.

The units of measure used in this course are the standard S.I. units that are used throughout

most of the Western world. Each unit has a name, like “volt” or “ampere”, and a

corresponding abbreviation, like “V” for volt and “A” for ampere. This saves time when

writing quantities – for example a current of “10 A” rather than “10 amperes”.

There are also a number of standard prefixes, which are used to indicate quantities a thousand

or a million or more times bigger or smaller than the basic unit. For example, the prefix

“milli” which is abbreviated “m” means “one thousandth of”, so one milligram – written as “1

mg” – means one thousandth of a gram. The following prefixes are widely used in

electronics:

Name Abbreviation Scale Factor Scientific Notation

pico p ÷ 1 000 000 000 000 10-12

nano n ÷ 1 000 000 000 10-9

micro µ ÷ 1 000 000 10-6

milli m ÷ 1 000 10-3

kilo k * 1 000 103

mega M * 1 000 000 106

giga G * 1 000 000 000 109

Scientific Notation

The column headed “scientific notation” may not be familiar to you. Because scientists workwith very small and very large numbers, it would be inconvenient for them to have to keep

writing many zeroes after the large numbers, or a decimal point and many zeros before the

small numbers. So they use the fact that multiplying by ten to the power of any positive

number effectively adds that many zeros at the end of the number. So for example the speed

of light is about 3 * 108 m/s which means “3 followed by 8 zeros”, or 300 000 000 m/s.

Another way of thinking of this is that it is equivalent to moving the decimal point 8 places to

the right, and introducing as many zeros as are necessary to do so. This is helpful when the

number already has a decimal point, for example “2,998 * 108”. Then you can’t simply thing

of adding zeros, since adding 8 zeros to “2,998” would give you “2,998 000 000 00” which

represents the same number (although to a greater precision). However if you instead think

about moving the decimal point 8 places to the right and adding zeros as necessary you getthe correct result, which is 299 800 000. The power of ten – in this case, 8 – is known as the

“exponent” and most scientific calculators have a key marked “E” or “Exp” which is used to

enter numbers in this format.

Similarly, a negative exponent means you move the decimal point that number of places to

the left , again filling in zeros as required. So for example, 1,6 * 10-19

is equivalent to 0,000

000 000 000 000 000 16, a very small number indeed. (If you were wondering, it is the charge

on an electron, in Coulombs.)

SummaryThis module has introduced the concepts of electric charge, electric current, and electric

potential. You have seen how the atomic structure of materials allows electric currents to flow

through some materials, which we call conductors, but not through others, which we call


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insulators. You have learnt the meaning of the prefixes that are used to scale units by powers

of ten, and to understand numbers written in scientific notation.

Revision Questions1. One of the following is not an electrical conductor:

a. Silver. b. Aluminium.

c. Copper.

d. Mica.

2. One of the following is not an electrical insulator:

a. Mica.

b. Ceramic.

c. Plastic.

d. Copper.

3. The unit of electrical potential is the:

a. Ampere. b. Amp.

c. Voltaire.

d. Volt.

4. A current of 15 A is equivalent to:

a. 1.5 * 10-5

A.

b. 15 * 10-5 A.

c. 1.5 * 106 A.

d. 15 * 106A.

5. A voltage of 20 000 V could be expressed as:

a. 20 µV.

b. 20 mV.

c. 20 kV.

d. 20 MV.

6. The charge carriers in solid copper that allow it to conduct electricity are:

a. Positively charged copper ions.

b. Negatively charged copper ions.

c. Positively charged electrons.

d. Negatively charged electrons.

7. Conventional current flows:a. In the same direction as electrons are moving.

b. In the opposite direction to the flow of electrons.

c. At right angles to the flow of electrons.

d. From negative to positive.

8. An electric current always consists of:

a. A flow of electrons.

b. A flow of neutrons.

c. A flow of protons.

d. A flow of charge.


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Radio Amateur Examination Manual Chapter 3 - Resistance and Ohm’s Law


Chapter 3 - Resistance and Ohm’s Law

In the last module we learnt that an electric current is a flow of charge that is caused by a

potential difference between two points. We also saw that the greater the electric potential

between two points joined by a conductor, the greater the current that would flow through the

conductor.

However the electric potential between two points is not the only factor that determines the

size of the current flowing between them. The current flow is also affected by a quality of the

conductor, known as its resistance. The resistance of a conductor can be thought of as being

the extent to which it resists the flow of current. The greater the resistance of a conductor, the

lower the current that will flow through it for a given potential difference. Conversely the

lower the resistance of the conductor, the greater the current that will flow through it for a

given potential difference.

The German physicist Georg Ohm (1789-1854) discovered that the potential difference across

a conductor is proportional the current that flows through the conductor. In other words if the

current flowing through a conductor doubles then the voltage across that conductor willdouble. Conversely if the current through the conductor halves then the voltage across the

conductor will also be halved.

Mathematically, this can be expressed by saying that the voltage across the conductor is equal

to the current through the conductor multiplied by some constant (for that particular

conductor). Ohm called this quantity the “resistance” of the conductor,

voltage = current * resistance

This relationship is known as “Ohm’s Law”.

The unit of resistance is the ohm. The abbreviation for the ohm is the Greek letter omega,which is written as Ω. A conductor has a resistance of one ohm if the application of a

potential difference of one volt across the conductor causes a current of one ampere to flow

through the conductor.

Resistance may be thought of as the opposition to the flow of electric current through a

conductor or electric circuit.

Symbols in Mathematical EquationsIn order to save time when writing out equations, it is common practice to use symbols to

represent quantities rather that writing out the full names of quantities like “voltage” and

“resistance” every time.

Certain symbols are commonly used to represent particular quantities. For example, “V” is

commonly used to represent an electric potential (voltage), and “R” is usually used to

represent a resistance. A current is usually not represented by “C” (which had already been

assigned another meaning in physics, the speed of light) but instead by “I”. Using these

symbols instead of the full names of the quantities, Ohm’s law us usually written as:

Ohm’s Law: V = I R

Note that the multiplication sign between “I” and “R” is also omitted. In mathematics when

two symbols are written next to each other it is assumed that they are to be multiplied

together.


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This form of Ohm’s law is convenient if you know the current flowing through a conductor

and the resistance of the conductor, and want to calculate the electrical potential (voltage)

across the conductor. It shows that you can calculate the voltage by multiplying the current by

the resistance.

For example, if a current of 5 A is flowing through a conductor with a resistance of 2 Ω then

the electric potential (voltage) across the conductor can be calculated by replacing the “I”

with 5 and the “R” with 2 in the equation for Ohm’s law, giving

V = 5 * 2

= 10 V

Note the somewhat confusing use of “V” both as the symbol for electric potential (voltage)

and also as the abbreviation for the unit “volt”. In this equation, the V on the left hand side

(before the equals sign) is the symbol for electric potential. The V after the number 10 is the

abbreviation for the unit, volts. The two meanings are not the same and you should take care

not to confuse them. You should be able to work out the correct meaning from the context in

which the “V” appears.

The symbol E is also used for electric potential. So you may see Ohm’s law written as E = I R

instead of V = I R.

Rearranging Ohm’s LawThis is all well and good if you know the current and the resistance and want to calculate the

voltage. However Ohm’s law can also be used to find either the current or the resistance if

both the other quantities are known. This is done by using simple algebra to rearrange Ohm’s

law as follows:

V = I R

By dividing both sides by I you get

V/I = R

and R = V/I

This can be used to calculate the resistance of a conductor given the electric potential

(voltage) across the conductor and the current flowing through it. Similarly, if you divide both

sides of the original equation by R you get

V/R = I

and I = V/R

In this form, Ohm’s law can be used to calculate the current flowing through a conductor

given the electrical potential (voltage) across the conductor and the resistance of the

conductor. You need to be able to use any of these three forms of Ohm’s law in the

examination.

SummaryOhm’s law states that the electric potential across a conductor is proportional to the current

flowing through the conductor. It can be written as V = I R, where R is a constant of

proportionality that is known the resistance of the conductor. Resistance may be thought of as

the opposition to the flow of electric current through a conductor or electric circuit.

Resistance is measured in ohms, with the abbreviation Ω. Ohm’s law can be used to find the


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electric potential across a conductor, or current flowing through the conductor, or the

resistance of the conductor provided that the other two quantities are known.

Revision Questions1 The opposition to the flow of current in a circuit is called:

a. Resistance. b. Inductance.

c. Emission.

d. Capacitance.

2 The current through a 100 Ω resistor is 120 mA. What is the potential difference

across the resistor?

a. 120 V.

b. 8,33 V.

c. 83,33 V.

d. 12 V.

3 The resistance value of 1 200 Ω can be expressed as:

a. 12 k Ω.

b. 1,2 k Ω.

c. 1,2 MΩ.

d. 0,12 MΩ.

4 How can the current be calculated when the voltage and resistance in a dc circuit

is known?

a. I = E / R.

b. P = I * E.

c. I = R * E.

d. I = E * R.

5 A 12 V battery supplies a current of 0,25 A to a load. What is the input resistance

of this load?

a. 0,02 Ω.

b. 3 Ω.

c. 48 Ω.

d. 480 Ω.

6 If 120 V is measured across a 470 Ω resistor, approximately how much current is

flowing through this resistor?

a. 56,40 A.

b. 5,64 A.

c. 3,92 A.

d. 0,25 A.

7. How can the voltage across a resistor be calculated when the resistance of andcurrent flowing through the resistor are known?

a. V = I / R.

b. V = R / I.

c. V = I R.

d. V = I2 R.

8. The law that relates the current flowing through a conductor to the electricpotential applied across the conductor is known as:


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a. Kirchoff’s Current Law.

b. Kirchoff’s Voltage Law.

c. Kirchoff’s Current and Voltage Law.

d. Ohm’s Law.


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Radio Amateur Examination Manual Chapter 4 - The Resistor and Potentiometer


Chapter 4 - The Resistor and Potentiometer

Electronic circuits are usually constructed from components that can be purchased at

electronics outlets. One such component is the resistor , which is simply a conductor that has a

known resistance. Resistors are available in values ranging from a fraction of an ohm to

several hundred mega-ohms.

Resistors also come in different tolerances. The tolerance shows how close the actual value of

the resistor is guaranteed to be to its nominal value. For example, the actual resistance of a 1

k Ω resistor with a tolerance of 5% could range from 950 Ω (1 k Ω - 5%) to 1 050 Ω (1 k Ω +

5%).

Resistors also come in various power ratings. As you will see in a couple of modules time, the

power dissipated by a resistance depends on the current flowing through the resistance and

the voltage across the resistance. In order to cater for different requirements, resistors are

usually available in power ratings from one eighth of a watt (0,125 W) to 5 W or more.

All electric components have symbols that can be used to draw diagrams showing how thecomponents should be connected to create a particular circuit. These diagrams are known as

“circuit diagrams” and the symbol for a resistor in a circuit diagram is:

In circuit diagrams, a plain line is used to represent a connection between two or more

components, so the lines coming out of the left and right of the resistor represent its

connections to the rest of the circuit. The resistor itself is the rectangle between these lines. In

older circuit diagrams you may also see a resistor represented as a zigzag line, but we will not

use that symbol. This symbol represents a simple fixed resistance. It has two connections

(represented by the lines at the left and right) and there is a known resistance between theseconnections.

Different Types of ResistorResistors come in several different types, which are suited to specific applications:

Carbon Film resistors are the most common, inexpensive, general-purpose resistors.

They typically have a tolerance of ±5% and power ratings from 0,125 W to 2 W.

Metal film resistors are often used when tighter tolerance is required (i.e. the resistor

is guaranteed to be closer to the nominal value). Metal film resistors typically have

tolerances of ±1% or better and power ratings from 0,125 W to 0,5 W.

Wire wound resistors are used in D.C. applications when high power ratings are

required. They are available in tolerances of ±5% or ±10% with power ratings from

2,5 W to 20 W or more. Note that wire wound resistors should never be used in

radio-frequency applications because they have unacceptably high inductance. (You

will learn about inductance in a future module).

Resistor networks consisting of a number of resistors in various circuit configurations

are supplied in packages that look like integrated circuits. They are intended for low-

power applications and are especially useful when you need many resistors of the

same value.


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The Resistor Colour CodeResistors are very small components, often only a few millimeters long, so if the value of a

resistor (its nominal resistance, in ohms) were printed on the resistor it would be very difficult

to read. So instead of printing the value onto resistors, a standard colour code is used where

the value of the resistance is represented by three coloured bands, and the tolerance of the

resistor by a fourth band. The following diagram represents not the circuit symbol for aresistor, but rather the physical resistor itself, showing the location of the colour bands.

From left to right the first two bands represent the first two digits in the value of the resistor.

In this case, brown represents “1” and black represents “0” so the first two digits of the value

are “10”. The third colour band – red in this case – represents the number of zeros that should

be added after the first two digits in the value (in other words, the exponent in scientificnotation). Since red represents the value “2”, two zeros must be appended to the first two

digits, giving a value of 1000 Ω or 1 k Ω.

The last band, the gold one at the far right hand side, gives the tolerance of the resistor. Since

gold means ±5%, the actual value of the resistor may range from 5% below the nominal value

of 1 k Ω to 5% above the nominal value.

Colour Digit Multiplier Tolerance

Black 0 * 1

Brown 1 * 10 1%

Red 2 * 100 2%Orange 3 * 1 000

Yellow 4 * 10 000

Green 5 * 100 000

Blue 6 * 1 000 000

Violet 7 * 10 000 000

Grey 8 * 100 000 000

White 9 * 1 000 000 000

Gold 5%

Silver 10%

For each colour the table shows you the digit that it represents when it occurs in the first two

bands, the multiplier it represents when it appears in the third band, and the tolerance that it

represents when it occurs in the last band.

Resistors with tight tolerances, such as 1% or 2% resistors, may have an extra band in the

colour code. In this case, the first three bands represent the first three digits of the value so

that the value of the resistor can be represented more precisely. The remaining bands

represent the multiplier and tolerance as before.

Expressing Resistor ValuesBecause resistors are very common components, a couple of shortcuts may be taken when

writing resistor values. The first is that the “ohm” or Ω abbreviation for the unit may be

omitted, so a 10 k Ω resistor may be referred to just as “10k”. The second is that the k or M

(for kilo and mega respectively) may be written where the decimal point would normally be,

Brown Black Red Gold


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and the decimal point omitted altogether. So a 3,3 k Ω resistor might be written as “3k3”, and

a 1,5 MΩ resistor as “1M5”. The character “R” is also sometimes used in place of the decimal

point when there is no scale factor. For example a 1,5Ω resistor might be written as “1R5”.

The Potentiometer

A related component is the potentiometer, which has a variable resistance. This is typicallyconstructed as a circular carbon track with a known resistance and a wiper that can be moved

over the track by turning a control knob. The resistance from one side of the track to the other

remains constant, but the resistance between either side and the wiper depends on the position

of the control knob. The symbol for a potentiometer is shown below.

The two ends of the carbon track are represented by the connections at the top and bottom of

the diagram. The resistance between these points is fixed. The arrowhead represents the

wiper. The three terminals “A”, “B” and “W” (for “wiper”) are labeled so that they can be

referred to in the explanation below. They are not usually labeled in this way.

Let us assume that the potentiometer has a value of 10 k Ω (10 000 Ω). That means that theresistance between A and B is always 10 k Ω. When the wiper is in a central position, as

represented in the diagram, then the resistance between A and W would be about half of this –

say 5 k Ω, and the resistance between B and W would be the other half of the resistance, also 5

k Ω.

Suppose we turn the control knob so the wiper is closer to A than to B. Then the resistance

between A and W would be less than half, say 2 k Ω. The resistance between B and W would

be the remainder of the 10 k Ω total resistance, in this case 8 k Ω. Similarly, if we set the wiper

all of the way over to B then the resistance between B and W would be 0 Ω (nothing), while

the resistance between A and W would be the entire 10 k Ω.

So the resistance between A and W and the resistance between B and W when added together

always equal the resistance from A to B, which is the value of the potentiometer.

Potentiometers are often used as controls on electronic equipment, for example the volume

control on an audio amplifier or radio receiver. There is also another symbol for a

potentiometer:

A

B

Wi er


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In this symbol, only the top and bottom lines represent connection points. The line with the

arrow point does not represent a separate connection, but rather means that the resistance is

variable. This typically represents exactly the same component as the more usual three-

terminal symbol shown above. However only two of the terminals are used: one side of the

carbon track and the wiper. The other side of the carbon track is left unconnected.

Although the symbols for the potentiometer are drawn vertically, while the symbol for the

resistor is drawn horizontally, this was purely for convenience. Any of the symbols, like most

electronics symbols, can be drawn either horizontally or vertically.

SummaryThe resistor is an electronic component with a defined resistance, tolerance and power rating.

The tolerance is the percentage by which the actual resistance may deviate from the nominal

value of the resistor. The value and tolerance of resistors is represented using the resistor

colour code. The potentiometer is a variable resistor.

Revision Questions

1. A potentiometer is a:

a. Meter. b. Variable resistor.

c. Battery.

d. Capacitor.

2. How can you determine a carbon resistor's electrical tolerance rating?

a. By using a wavemeter.

b. By using the resistor's colour code.

c. By using Thevenin's theorem for resistors.

d. By using the Baudot code.

3. Which of the resistors below (each identified by its colour coding) would be

nearest in value to a 4k7 resistor? a. Orange violet orange.

b. Yellow green red.

c. Orange violet red.

d. Yellow green orange.

4. What would the colour code be for an 820 Ω resistor, excluding the tolerance

band?

a. grey red black.

b. grey red brown.

c. red grey black.

d. red grey brown.


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5. What would the value of a resistor with the colour code orange orange orange be?

a. 333 Ω.

b. 3,3 k Ω.

c. 33 k Ω.

d. 330 k Ω.

6. A 10 k Ω resistor has a gold tolerance band. The actual resistance may be:

a. From 9 000 to 11 000 Ω.

b. From 9 500 to 10 500 Ω.

c. From 9 800 to 10 200 Ω.

d. From 9 900 to 10 100 Ω.

7. A 2,2 Ω resistor might be labeled on a circuit diagram as

a. 2k2.

b. 2M2.

c. 2R2.

d. 22R.

8. The label “4M7” on a circuit diagram could refer to:

a. A resistance of 4,7 mega ohms.

b. A current of 4,7 mega amps.

c. A voltage of 4,7 mega volts.

d. Any of the above.

9. The circuit diagram for a resistor is:

a. A straight line.

b. A circle containing a zig-zag line.

c. A rectangle.

d. A triangle.

10. Which of the following types of resistor would not be suitable for radio-frequency

applications?

a. A carbon film resistor.

b. A metal film resistor.

c. A wire-wound resistor.

d. A resistor network.


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Radio Amateur Examination Manual Chapter 5 - Direct Current Circuits


Chapter 5 - Direct Current Circuits

Direct current (abbreviated “D.C.”) means a current that is flowing constantly in one

direction. It is contrasted to alternating current (“A.C.”) like the mains supply, where the

direction in which the current flows changes periodically, usually many times every second.

Despite the apparent contradiction in terms, it is common practice to speak of a “D.C.voltage” to mean a constant voltage, and an “A.C. voltage” to mean a voltage that is reversing

polarity (i.e. exchanging positive and negative terminals) periodically. Although for the

moment we shall only consider direct current (D.C.) circuits, when we come to alternating

current (A.C.) circuits we will see that the same principles apply

Remember that “voltage” is a commonly used term meaning electric potential, and this will

be used in preference to the term “electric potential” for the remainder of these notes, since

this is how it is most commonly referred to.

Kirchoff’s LawsGustav Kirchoff (1824-1887) formalized two very simple laws that allow us to analyze

electric circuits. The first is known as Kirchoff’s current law.

Kirchoff’s Current Law: At any point in a circuit where two or more wires are joined, the

sum of the currents flowing into the point is equal to the sum of the currents flowing away

from the point.

For example, consider the diagram above, which shows two resistors connected “in parallel”.

The arrows on the lines represent currents. A current I IN flows into the circuit from the left,

divides into two currents I1 and I2, which flow through resistors R 1 and R 2 respectively. After

flowing through the resistors, the currents join again together to give IOUT.

Note that this is not a complete circuit, as we have not shown the source of electric potential

that is causing the current to flow. We must assume that there is some voltage source

connected so that its positive terminal is connected to the wire on the left hand side of the

diagram and its negative terminal is connected to the wire on the right hand side of thediagram in order to make the current flow.

Applying Kirchoff’s current law to the point where IIN splits into I1 and I2, we see that the sum

of the currents flowing into the point – in this case there is only one current, I IN – must equal

the sum of the currents flowing out of the point – in this case, I1 + I2. One way to look at this

is that current is a flow of charge, and charge cannot accumulate at a point, so charge must

flow out of the point just as fast as it flows in.

In our analogy with a water pipe, if you put a “T” connector on a pipe then the rate at which

the water flows out of the two output pipes combined must equal the rate at which the water is

flowing into the input pipe, since the water that is coming in has to go somewhere and it

cannot accumulate in the T connector.

IIN

I2

I1

R 2

R 1

IOUT


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So in the diagram above we have

IIN = I1 + I2

Referring now to the point where I1 and I2 join together to form IOUT, we can again apply

Kirchoff’s current law which says that the sum of the currents flowing into the point – that is,

I1 + I2 – must equal the sum of the currents flowing out of the point, in this case just I OUT. So

this application of Kirchoff’s Current Law gives us

I1 + I2 = IOUT

Because both equations have “I1 + I2” on one side of the equals sign, we can combine them to

get

IIN = IOUT

which makes sense because the charge that is flowing in on the left hand side has to go

somewhere, and the only place for it to go is out the right hand side of the diagram.

The second of Kirchoff’s laws is Kirchoff’s Voltage Law. It can be formulated in two

different but equivalent ways. The first formulation, which is the most useful, is as follows.

Kirchoff’s Voltage Law (1): The voltage between any two points in a circuit is equal to the

sum of the voltage drops along any path connecting those points.

This requires some explanation. Consider the circuit below:

A

+

B

The symbol on the left hand side of the diagram represents a battery. The long line always

represents the positive terminal, but has been labelled with a “+” sign to make it clear. The

battery voltage has also been labelled as VB. The battery is generating a voltage across R 1 and

R 2, which are connected “in series”, and across R 3, which is connected “in parallel” with R 1

and R 2.

The voltage applied by the battery will cause a current to flow through R 1 and R 2 and another

(possibly different) current to flow through R 3. However we know from Ohm’s law that when

a current flows through a resistance there will be a voltage across the resistance. The voltageacross a resistance is often referred to as a “voltage drop”. The voltage drops across R 1, R 2

R 1 V1

V2 R 2

R 3 V3

VB


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and R 3 have been labelled as V1, V2 and V3 respectively. The lines with arrowheads are used

to indicate what points the voltage drop is across. Note that by convention the arrowhead

points towards the positive side, which means that the arrows point in the opposite direction

from the direction in which current is flowing in the circuit. (In this circuit, the currents in the

resistors are all flowing from top to bottom.)

Voltage Drop: the potential difference across a component like a resistor caused by the

current flowing through the component.

So what does Kirchoff’s Voltage Law tell us about the circuit? Consider points A and B in the

diagram. Kirchoff’s voltage law tells us that the voltage between points A and B is equal to

the sum of the voltage drops along any path connecting A and B. If we call the voltage

between A and B “VAB”, then applying Kirchoff’s Voltage law to the three different paths

between A and B gives us:

VAB = VB (from the path through the battery)

VAB = V1 + V2 (from the path through R 1 and R 2)

VAB = V3 (from the path through R 3)

In other words, the same voltage is found across the battery, across the series combination of

R 1 and R 2 and across R 3. Thinking of it in another way, the battery voltage VB has been

applied across both the series combination of R 1 and R 2 and across R 3. The concept is very

simple and straightforward, and you should be able to apply it intuitively and hardly ever

have to think about its formal statement as Kirchoff’s Voltage Law.

At the beginning of the section it was mentioned that there are two different although

equivalent formulations of Kirchoff’s voltage law. The second is:

Kirchoff’s Voltage Law (2): The sum of the voltage drops around any closed circuit is zero.

This is somewhat less intuitive than the original formulation. Suppose we take a clockwise

trip around the outside circuit in the diagram above, starting and ending at point A. We first

go “through” the resistor R 3, and so V3 is our first voltage drop. Staying on the outside circuit

(and so ignoring R 1 and R 2), we next come to the battery. However the voltage across the

battery, VB, is not actually a voltage drop because we are moving from the negative terminal

to the positive terminal so the voltage is increasing . However we can’t just ignore it, so we

instead count the battery voltage VB as a negative voltage drop and add -VB to our “sum of

voltage drops”. Since adding the negative of a number is the same as subtracting that number

we get:

sum of voltage drops = V3 - VB

However we have already seen that V3 and VB are equal, so the sum equals zero and Kirchoff

is happy!

Resistors in SeriesHaving mastered Ohm and Kirchoff’s laws, we can use these to derive some simple and well-

known results. The first is the formula for calculating the effective resistance of two resistors

in series. Consider the following circuit:


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I

+

It shows two resistors connected “in series” so that the same current flows through both of the

resistors, although the voltages across each resistor may be different. The current flowing inthe circuit is I, while the voltages across R 1 and R 2 are V1 and V2 respectively. The voltage

across both resistors combined as VTOTAL. The battery is only shown for completeness, to

show how the current is being made to flow in the circuit.

Suppose we want to replace the two separate resistors R 1 and R 2 by a single resistor, which

will have the same effect. What value of resistor should we choose?

Note that the derivation below is provided for interest only and will not be examined. You

only need to know the result that appears in italics at the bottom of this section.

From Ohm’s law,

V 1 = I R1

and V 2 = I R2

From Kirchoff’s Voltage Law

V TOTAL = V 1 + V 2

Replacing V 1 and V 2 in this formula with the values from Ohm’s law,

V TOTAL = I R1 + I R2= I (R1 + R2 )

But this is just Ohm’s law for a resistor with the value R1 + R2. In other words, the resistors R1and R2 together behave just as though they were a single resistor with the value R1 + R2. This

gives us the result we are looking for:

When two or more resistors are connected in series, the combined resistance is the sum of the

individual resistances.

Although we have showed this for two resistors, it is easy to generalize the result to any

number of resistors. This is left as an exercise for the reader. (Hint: you don’t need Kirchoff’s

and Ohm’s laws, you can just use the result for two resistors and the properties of addition.)

For example, if three resistors with the values 1k Ω, 2k Ω and 4 k Ω were connected in series

the combined resistance would be 7k Ω.

V1

V2

VTOTAL

R 1

R 2


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Resistors in ParallelAnother way of connecting components is to connect them in parallel , so the same voltage

appears across each of the components although the currents through them may (and probably

will) differ.

Consider the following circuit, which shows two resistors connected in parallel. (This time thesource of the potential difference has been omitted – perhaps we should describe it as a

“partial circuit”.)

The same voltage, V appears across both resistors. The currents through them are I 1 and I 2,

while the total current through both resistors combined is I TOTAL.

Once again the derivation is provided for interest only and is not required for theexamination.

Using Ohm’s law,

I 1 = V / R1

and I 2 = V / R2

According the Kirchoff’s Current Law,

I TOTAL = I 1 + I 2

Substituting the values of I 1 and I 2 obtained using Ohm’s law,

I TOTAL = V / R1 + V / R2

Applying Ohm’s law to the whole circuit,

V / R PARALLEL = I TOTAL

= V / R1 + V / R2

Where R PARALLEL is the equivalent resistance of the two resistors in parallel. Dividing by V ,

1 / R PARALLEL = 1 / R1 + 1 / R2

V R 1 R 2

I1 I2

ITOTAL

ITOTAL


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This is the result we were looking for, as it shows the relationship between the value of the

combined parallel resistance and the individual resistances. It is not as easy to put into words

as it was for resistors in series, but I’ll give it a go:

When two or more resistors are connected in parallel, the reciprocal of the equivalent

parallel resistance is the sum of the reciprocals of the individual resistances.

(Note: the reciprocal of a number is one divided by that number.)

Of course, this leaves us with the reciprocal of the value we are looking for. Fortunately it is

simple to convert the reciprocal of a number back into the number itself – just calculate the

reciprocal of the reciprocal and this will be the original number! For example, suppose a 220

Ω resistor is connected in parallel with a 330 Ω resistor. We can find the equivalent combined

resistance of the two resistors in parallel as follows:

1 / R PARALLEL = 1 / R1 + 1 / R2

= 1/220 + 1/330

= 0,004 55 + 0,003 03= 0,007 58

So R PARALLEL = 1 / 0,007 58 (the reciprocal of the reciprocal!)

= 132 Ω

There is a short cut that can be applied when all the resistances in parallel have the same

value. In this special case, if the resistors all have the value R and there are N resistors

connected in parallel, then the equivalent resistance is R/N . We leave the proof of this as an

exercise for the interested reader.

Practical ExampleA “dummy load” is a high-powered resistor that can be connected to the antenna port of a

transmitter. It enables the transmitter to be tested or aligned without actually having to

transmit a signal. Transmitting a signal during testing when not absolutely necessary would

cause interference and would be considered extremely bad manners by amateurs.

Commercial dummy loads are available but they are quite expensive. An alternative for the

amateur is to make your own. Unfortunately the most commonly available suitable resistors

only have a power rating of 2 W, while most transceivers will put out 100 W and would

incinerate a 2 W resistor. One solution is to use fifty 2 W resistors all connected in parallel, so

that each handles one fiftieth of the transceiver’s power. If the resistors are each 2 500 Ω

(2k5) then the effective resistance of 50 resistors in parallel is 2500 / 50 = 50 Ω, which is the

correct value to match most amateur transceivers.

Remember that you will also want to shield the dummy load to prevent it from inadvertently

becoming a fully functional transmitting antenna. This can be achieved by enclosing it in a

metal baking powder tin which is chosen because it has a screw-on lid. Drill a hole in the

bottom of the tin to accommodate a SO235 (UHF) connector and attach the centre conductor

to a piece of stiff wire running down the centre of the tin. Then solder the resistors between

this central conductor and the body of the tin. In this way the tin also serves as a heat sink for

the resistors as well as a shield for the dummy load.


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The Voltage DividerTwo resistors in series can be used as a voltage divider . Consider the circuit below:

I

R 1

VIN

R 2 VOUT

This shows two resistors connected in series as before. However this time, we are measuring

the voltage VOUT across one of the resistors. Our task is to find this output voltage in terms of

the input voltage applied across both resistors.

Using our formula for resistors in series, we know that the total combined resistance of R1 and

R2 in series is R1 + R2. We can apply Ohm’s law to the input voltage and the combined

resistance of R1 and R2 in series to find the input current I :

I = V IN / (R1 + R2 )

Now, if we assume that negligible current is drawn from the output, then the same current I

flows through both resistors. Hence we can find the voltage across R2, which is the output

voltage, using Ohm’s law:

V OUT = I R2

Substituting the value we obtained for I by applying Ohm’s law to the series combination of

R1 and R2 we get

V OUT = (V IN / (R1 + R2 )) R2

= V IN R2 / (R1 + R2 )

The circuit is known as a “voltage divider” because the output voltage is proportional to but

smaller than the input voltage, so the effect of the circuit is to divide the input voltage by a

constant (greater than 1).

SummaryKirchoff’s Current Law states that any point in a circuit where two or more wires are joined,

the sum of the currents flowing into the point is equal to the sum of the currents flowing away

from the point. His Voltage Law states that the voltage between any two points in a circuit is

equal to the sum of the voltage drops along any path connecting those points.


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We can use these laws in conjunction with Ohm’s law to calculate the equivalent values of

resistors in series and in parallel. When two or more resistors are connected in series, the

combined resistance is the sum of the individual resistances. When two or more resistors are

connected in parallel, the reciprocal of the equivalent parallel resistance is the sum of the

reciprocals of the individual resistances.

The voltage divider consists of two resistors in series with an output voltage measured across

one of the resistors. The formula for the output voltage of a voltage divider is:

V OUT = V IN R2 / (R1 + R2 )

Revision Questions

1 Two 10 k Ω resistors are connected in parallel. If the voltage from a battery across

the resistors sets up a current of 5 mA in the one resistor, how much current flows

in the second?

a. 10 mA.

b. 2 mA.c. 20 mA.

d. 5 mA.

2 Two resistors are connected in series to a 9 V battery. The voltage across one of

the resistors is 5 V. What is the voltage across the other resistor?

a. 4 V.

b. 5 V.

c. 9 V.

d. 13 V.

3 In a parallel circuit with a voltage source and several branch resistors, what

relationship does the total current have to the current in the branch currents?

a. The total equals the average of the branch current in each resistor.

b. The total equals the sum of the branch currents in each resistor.

c. The total decreases as more parallel resistors are added to the circuit.

d. The total is calculated by adding the voltage drops across each resistor and multiplying

the sum by the total number of all circuit resistors.

4 Two resistors are connected in series. The combined resistance is 1 200 Ω. If one

of the resistors is 800 Ω, what is the value of the other?

a. 1 000 Ω.

b. 800 Ω.

c. 400 Ω.d. 1 200 Ω.

5 A 100 Ω resistor is connected in series with a 200 Ω resistor. The equivalent

resistance of the two resistors is:

a. 100 Ω.

b. 200 Ω.

c. 300 Ω.

d. 400 Ω.


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6 A 100 Ω resistor is connected in parallel with a 200 Ω resistor. The equivalent

resistance of the two resistors is:

a. 50 Ω.

b. 67 Ω.

c. 75 Ω.

d. 300 Ω.

7 Two light bulbs are connected in series. Which of the following statements is

necessarily true:

a. The current flowing through each of the bulbs is identical.

b. The voltage across each of the bulbs is identical.

c. The resistance of each of the bulbs is identical.

d. The light given off by each of the bulbs is identical.

8 Two light bulbs are connected in parallel to the mains. One of them blows, and

becomes an open circuit (i.e. no current can flow through it). What will happen to

the current flowing through the bulb that is still working.

a. Twice the current as before will flow through the working bulb. b. No current will flow through the working bulb.

c. The same current as before will flow through the working bulb.

d. Half the current as before will flow through the working bulb.

9 The output voltage from a voltage divider with two equal resistances will be:

a. The same as the input voltage.

b. One quarter of the input voltage.

c. Half the input voltage.

d. One third of the input voltage.

10 A dummy load is made by connecting forty-four 2k2 resistors in parallel. The

resistance of the dummy load is:

a. 20 Ω.

b. 50 Ω.

c. 75 Ω.

d. 100 Ω.


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Radio Amateur Examination Manual Chapter 6 - Power in D.C. Circuits


Chapter 6 - Power in D.C. Circuits

Power Dissipation in ResistancesWhen a current flows through a resistance, the resistance will dissipate (“use up”) power and

generate heat. This principle is used in many electrical devices, for instance in electric bar

heaters and kettles, where the elements are just resistances with suitable power handling andheat transfer abilities.

To calculate the power dissipated by a resistance, you multiply the voltage (electric potential)

across the resistance by the current flowing through the resistance, so

P = V I

It is easy to see why. Remember that the electric potential between two points is the amount

of energy that it would take to move one unit of charge from the point of lower potential to

the point of higher potential. Now that we are allowing the charge to flow from the point of

higher potential back to the point of lower potential, this energy is recovered, usually in the

form of heat. Since current is the rate of flow of charge, the greater the current the greater the

energy that will be given off each second, and hence the greater the power.

For example, suppose an electric kettle draws 5 A at 240 V. Its power consumption is

calculated as follows:

P = V I

= 240 * 5

= 1 200 W

= 1,2 kW

(Of course kettles usually work off A.C. not D.C. power, but when we get to the section onA.C. power you will see that the same formula applies.)

Using Ohm’s Law With The Formula For PowerOf course Ohm’s law also deals with voltages and currents (as well as resistances), so it can

often be used together with the formula for power. For example, suppose that in the example

above we had instead been told that the kettle runs off 240 V and its element has a resistance

of 48Ω. We could then use Ohm’s law to calculate the current, since

I = V / R

= 240 / 48

= 5 A

The rest of the calculation would then proceed as above, giving us the same answer of 1,1

kW. Another way is to combine Ohm’s law and the formula for power dissipation first, and

only bring the actual numbers in at the end.

The formula for power is

P = V I

But according to Ohm’s law, we also know that

I = V / R


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So we can replace the symbol “ I ” in the power equation with “V / R” to give

P = V V / R

And since V * V is just V2 (pronounced “V squared”), we end up with

P = V 2 / R

Applying this to the example, where V = 240 V and R is 48Ω, we get

P = 2402 / 48

= 57 600 / 48

= 1 200 W

= 1,2 kW

Which fortunately is the same answer as before.

In the same way, if you know the current flowing through a resistance and the value of theresistance, but not the voltage across it, then you can use Ohm’s law to calculate the voltage

across the resistance and then apply the formula for power to calculate the power dissipation.

Or these two steps can be combined in a single equation:

P = V I (the formula for power)

and V = I R (Ohm’s law)

so P = I I R

= I 2 R

This gives you a simple formula for calculating power from current and resistance:

P = I 2 R

For example, suppose a 50 Ω resistor has a current of 2 A flowing through it. The power

dissipated is:

P = I 2 R

= 22 * 50

= 4 * 50

= 200 W

Exercise

Use Ohm’s law to find the voltage across the resistor, and then the formula P = V I to

calculate the power dissipated by the resistor, and see if you get the same answer.

Matching Source and LoadAll real life voltage sources have some internal resistance. This can be represented as

follows, where the circle with a “V” in it represents a perfect voltage source, R SOURCE is the

resistance of the source, and R LOAD is the load resistance. (A load is something which the

circuit is delivering power to. Depending on the application it might be an antenna, an electric

motor, a light bulb or anything else that uses power.)


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R SOURCE

V R LOAD

An interesting question is what load resistance (i.e. what value of R LOAD) will result in the

maximum power transfer to the load?

If the load resistance is very low, then a lot of current will flow in the circuit, but the voltageacross the load will be small. If the resistance is high, then the voltage across the load will be

high, but the current through it will be low. Since P = V I both the current through the load

and the voltage across it are important for power transfer.

Although the mathematics is a bit beyond the level of this course, it turns out that the load

dissipates the maximum power when the load resistance is exactly equal to the source

resistance. In this case, the power dissipated by the load is V 2 / (4 R LOAD ). This is useful to

know when designing power sources such as power amplifiers. You should note, however,

that with a matched load the source dissipates just as much power as the load, so heat sinking

may be quite important!

SummaryThe power dissipated in a resistive load can be found using the formula P = V I . This can be

combined with Ohm’s law to give P = I 2 R and P = V

2 / R. In a simple resistor, this power

will be dissipated as heat.

All voltage sources have some internal resistance. The maximum power transfer from the

source to the load occurs when the load resistance is exactly equal to the source resistance.

Revision Questions 1 A light bulb is rated at 12 V and 3 W. The current drawn when used on a 12 V

source is:a. 250 mA.

b. 750 mA.

c. 4 A.

d. 36 A.

2 The DC current drawn by the final stage of a linear amplifier is 100 mA at 100 V.

How much power is consumed?

a. 100 W.

b. 1 kW.

c. 10 W.

d. 1 W.


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3 If a power supply delivers 200 W of electrical power at 400 V DC to a load, how

much current does the load draw?

a. 0,5 A.

b. 2,0 A.

c. 5 A.

d. 80 000 A.

4 The product of the current and what force gives you the electrical power in a

circuit?

a. Magnetomotive force.

b. Centripetal force.

c. Electrochemical force.

d. Electromotive force.

5 A resistor is rated at 10 W. Which of the following combinations of potential

difference and current exceeds the rating of the resistor?

a. 2 V, 100 mA.

b. 20 V, 200 μA.c. 1 kV, 25 mA.d. 10 mV, 2 A.

6 The starter motor of a motor car draws 20 A from the 12 V battery. How much

power does it use?

a. 2,4 W.

a. 24 W.

b. 240 W.

c. 2,4 kW.

7 What is the resistance of the motor in question 6?

a. 0,6 Ω. b 1 Ω.

c 6 Ω.

d 10 Ω.

8 The internal resistance of a car battery is found to be 0,2 Ω. Into what load

resistance will it deliver the maximum power?

a. 0,1 Ω.

b. 0,2 Ω.

c. 0,6 Ω.

d. 1,2 Ω.

9 At its peak, a lightning bolt has a voltage of 100 million volts and 10 000 A. How

much power does it deliver?

a. 109 W.

b. 1010

W.

c. 1011 W.

d. 1012

W.

10 A current of 2 mA is measure in a 1 k Ω resistor. How much power is the resistor

dissipating?

a. 2 mW.

b. 4 mW.

c. 2 W.d. 4 W.


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Radio Amateur Examination Manual Chapter 7 - Alternating Current


Chapter 7 - Alternating Current

IntroductionIn direct current (D.C.) circuits, the current always flows in one direction. This is because the

two terminals of the voltage sources used to power these circuits always have the same

polarity – one terminal (the positive one) is always positive with respect to the other terminal.This causes the current to flow in only one direction in the circuit.

However in other circuits, the direction in which the current flows is constantly changing. The

current flows first in one direction, then in the reverse direction, then in the original direction

again and so on, with the direction changing at regular intervals, usually many times each

second. The circuits are called alternating current (A.C.) circuits. Power for these circuits

may be supplied by alternating current (A.C.) power supplies, such as the mains supply. With

A.C. power supplies, there is no “positive” or “negative” terminal. Instead, one terminal will

be positive with respect to the other for a brief period, and then the roles will reverse and the

other terminal will become more positive for a brief period, and so on. Although the

abbreviation A.C. stands for “alternating current”, it is also used to refer to voltages, in

phrases such as “An A.C. Voltage” and “15 VAC.”.

The Sine WaveIf you were to plot the voltage or current in an A.C. circuit against time, there are many

possible shapes (known as “waveforms”) that this could take. For example:

Figure 1: A Triangular Wave

Figure 2: A Square Wave

However, when we analyze A.C. circuits, we normally think of the waveform as being a “sine

wave”. This is a waveform given by the mathematical equation:

V = V PEAK sin(2π ft)


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Where V PEAK is the peak voltage of the waveform, f is its frequency, t is time, π is themathematical constant “pi” (approximately 3,14) and sin is the trigonometric “sine” function.

The shape of a sine wave is shown below. Note that it is not two semi-circles, which is how it

is sometimes incorrectly drawn.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Figure 3: A Sine Wave

The reason why we deal mostly with sine waves in circuit analysis is because the Frenchmathematician Joseph Fourier (1768-1830) showed that any other waveform could be

decomposed into a number of sine waves of different frequencies. So if we know how a

circuit responds to a sine wave then we can easily calculate its response to any other

waveform using the technique known as Fourier analysis. A sine wave represents a “pure”

A.C. waveform that contains only a single frequency, known as the fundamental . Any other

waveform includes both the fundamental and harmonics, which are integral multiples of the

fundamental frequency.

Cycles and Half CyclesAn A.C. waveform consists of many identical cycles one after another. Figure 3 shows one

complete cycle of a sine wave, while Figure 1 shows two complete cycles of a triangular

waveform.

Question: How many cycles of a square wave are shown in Figure 2?

Usually electrical waveforms like A.C. voltages and currents are positive for half the time and

negative for the other half. When we want to refer just to the positive or negative period, we

speak of the “positive half cycle” and “negative half cycle”.

Period and FrequencyThe period of a waveform is the time taken for one cycle, which is usually expressed in

seconds, milliseconds or microseconds.

Definition: The period of a waveform is the time taken for one complete cycle.

90° 180° 270° 360°

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